Well it's a shove-or-check/fold spot.
I assume that he will not bet any 1pair or 2pair hands because he's afraid of us having flush or straight.
At the same time imo most 1pair hands fold, some 2pairs might call, but they might as well find a fold given how scary the board is.

So I'm check/folding, expecting to see him checking back quite often (and if he shoves I'm almost certain he has a flush).